A binary message m, where m is equal either to 0 or to 1, is sent...

A binary message m, where m is equal either to 0 or to 1, is sent over an information channel. Assume that if m = 0, the value s = −1.5 is sent, and if m = 1, the value s = 1.5 is sent. The value received is X, where X = s + E, and E ∼ N(0, 0.66). If X ≤ 0.5, then the receiver concludes that m = 0, and if X > 0.5, then the receiver concludes that m = 1.

If the true message is m = 0, what is the probability of an error, that is, what is the probability that the receiver concludes that m = 1? Round the answer to four decimal places.

If the true message is m = 1, what is the probability of an error, that is, what is the probability that the receiver concludes that m = 0?

A string consisting of 60 1s and 40 0s will be sent. A bit is chosen at random from this string. What is the probability that it will be received correctly?

Refer to part (c). A bit is chosen at random from the received string. Given that this bit is 1, what is the probability that the bit sent was 0?

Refer to part (c). A bit is chosen at random from the received string. Given that this bit is 0, what is the probability that the bit sent was 1?

Solutions

Expert Solution

orchestra answered 1 year ago

Next > < Previous

Related Solutions

When a message is sent electronically it is usually sent as a stream of bits, each...

When a message is sent electronically it is usually sent as a stream of bits, each of which can be either a 0 or a 1. If the digital channel is noisy then each bit has some probability of being flipped (ie changed from a 0 to a 1 or vice versa) resulting in a corrupted message. Assume that a message is being sent through a noisy channel where the probability that any individual bit will be flipped is 0.1....

Let M(x, y) be "x has sent y an e-mail message" and T(x, y) be "...

Let M(x, y) be "x has sent y an e-mail message" and T(x, y) be " x has telephoned y, " where the domain consists of all students in your class. Use quantifiers to express each of these statements. g. There is a student in your class who sent every one else in your class an email message. I answer ∃x( x ≠ y ∧ ∀? M (x, y) ) But answer on text book is ∃x( x ≠ y → ∀?...

2. i. Consider a binary source alphabet where a symbol 0 is represented by 0 volt...

2. i. Consider a binary source alphabet where a symbol 0 is represented by 0 volt and a symbol 1 is represented by 1 volt. Assume these symbols are transmitted over a baseband channel having uniformly distributed noise with a probability density function: px= {18 for-4≤x≤4 0 Assume that the single decision threshold T is in the range of 0 and l volt. If the symbols 0 and 1 are sent with probabilities p0 and 1- p0 respectively, derive...

solve tan^2 x =1 where x is more than or equal to 0 but x is less than or equal to pi

solev tan^2 x =1 where x is more than or equal to 0 but x is less than or equal to pi

For each of the following scenarios, identify the nonverbal message being sent and indicate if the...

For each of the following scenarios, identify the nonverbal message being sent and indicate if the sender and/or receiver should handle the matter differently: While you are talking to a client, she starts drumming her fingers on her desk. You are a new employee attending your first group meeting. When a man arrives after the meeting has started, others stand up to offer him a chair. When you make a suggestion at a group meeting, a colleague rolls her eyes....

Consider the ODE u" + lambda u=0 with the boundary conditions u'(0)=u'(M)=0, where M is a...

Consider the ODE u" + lambda u=0 with the boundary conditions u'(0)=u'(M)=0, where M is a fixed positive constant. So u=0 is a solution for every lambda, Determine the eigen values of the differential operators: that is a: find all lambda such that the above ODE with boundary conditions has non trivial sol. b. And, what are the non trivial eigenvalues you obtain for each eigenvalue

. We have the following algorithm. Algorithm Novel(X[0..m-1, 0..m-1]) //Input: A matrix X[0..m-1, 0..m-1] of real...

. We have the following algorithm. Algorithm Novel(X[0..m-1, 0..m-1]) //Input: A matrix X[0..m-1, 0..m-1] of real numbers for i←0 to m-2 do for j←i+1 to m-1 do if X[i,j] ≠X[j, i] return false return true a. What does this algorithm compute? b. What is its basic operation? c. How many times is the basic operation executed? d. What is the efficiency class of this algorithm?

A 60% mole Benzene and 40% mole Toluene mixture is sent to a distillation column, where it is separated into two equal streams.

A 60% mole Benzene and 40% mole Toluene mixture is sent to a distillation column, where it is separated into two equal streams. Calculate the composition of each stream, if the amount of benzene out of the top is 3 times greater than out the bottom.

A source transmitted a message through a noisy channel. Each symbol is 0 or 1 with...

A source transmitted a message through a noisy channel. Each symbol is 0 or 1 with probability p and 1 − p, respectively and is received incorrectly with probability 0 and 1. Errors in different symbol transmission are independent. (a) What is the probability that the kth symbol is received correctly? (b) What is the probability that the string of symbols 0111 is received correctly? (c) To improve reliability, each symbol is transmitted three times and the received string is...

For a hypothesis test, where ?0:?1=0 and ?1:?1≠0, and using ?=0.01 , give the following:

Consider the data set below. x 22 99 88 44 99 99 y 66 44 88 55 77 11 For a hypothesis test, where ?0:?1=0 and ?1:?1≠0, and using ?=0.01 , give the following: (a) The test statistic ?= (b) The degree of freedom ??= (c) The rejection region |?|> The final conclustion is A. There is not sufficient evidence to reject the null hypothesis that ?1=0 β 1 = 0 . B. We can reject the null hypothesis that...

Subjects